The last thing to check is wiring. It sounds like an intermittent short to ground that passes through a high resistance load path of some kind first when it makes contact, such that it acts like you turned a heater element on or something, and doesn't trip the breaker.
The wiring harness needs to be "wrung out", using a Digital Multimeter, first for shorts that appear spontaneously when the wire harnesses are jiggled at various places in the charging circuit.
If that doesn't find anything, the next test is Megger, or Meg-Ohmmeter checks, which puts high voltage/low current through wiring runs disconnected from the services, looking for MegOhm values that point to current leakage through the wiring insulation.
Usually you will put 200 or maybe 400 v though the disconnected wires, via the multimeter (milliamps of current), with resistance below some threshold indicating insulation breakdown.
Megger is a very common troubleshooting procedure on airliners, but may be rarely done on light airplanes, so I don't know if you'll even be able to find Megger specifications for the airplane's wiring harness in its documentation.
On transport airplanes, the normal sequence is throw parts at it, problem still comes back, wring out the wiring looking for direct shorts, then insulation breakdown checks as I described.
A 45 year old airplane is likely to have brittle wiring insulation, especially on the engine side of the firewall where all the heat is.